Analysis of Qualitative And Quantitative Rankings in Multicriteria Decision Making

Problems involved by social choices, as planning and environment management or risky situations, have as main tool for their solution decisional procedures based on multicriteria analysis. A crucial point in Multicriterial methods, as the Analytic Hierarchy Process, is given by the quantitative evaluations of alternatives with respect to a criterion C. These evaluations may involve pairwise comparison matrices and suitable methods have to be applied to them in order to get the quantitative ranking of the alternatives. In the real cases, because of several kind of errors, imprecisions or lack of coherence in the judgements, the comparison matrix may not enjoy the property of consistency and the rankings supplied by the different methods (right eigenvector method, arithmetic mean or geometric mean method) may not coincide or not agree with the expressed comparisons. So it is important to state a way to obtain the actual qualitative ranking and to compare with it the quantitative rankings provided by the mentioned methods. In this paper we give a review of the results related to the above questions for both ordinal and cardinal rankings.